SOLUTION: How does this work, what is this called? If I have a problem like: {{{ 2x^2+5x-3=0 }}} for some reason it was brought to me I can break up the 5x like so {{{ 2x^2+6x-1x-3=0 }} and

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How does this work, what is this called? If I have a problem like: {{{ 2x^2+5x-3=0 }}} for some reason it was brought to me I can break up the 5x like so {{{ 2x^2+6x-1x-3=0 }} and      Log On


   

Question 951644: How does this work, what is this called?
If I have a problem like: +2x%5E2%2B5x-3=0+ for some reason it was brought to me I can break up the 5x like so and thus x=1/2 and x=-3. Please help! what is this called how is it done?
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E2%2B5x-3=0+
is the same as
+2x%5E2+%2B+6x+-+x+-+3+=+0+
Group factor here
2x(x + 3) - 1(x + 3) = 0
note that now you can factor out (x+3) and you have
(x + 3)(2x - 1) = 0
Which would give you the solutions that you have, not sure what you call this

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How does this work, what is this called?
If I have a problem like: +2x%5E2%2B5x-3=0+ for some reason it was brought to me I can break up the 5x like so and thus x=1/2 and x=-3.
==========================
It's called quadratic equation, and equation of degree 2.
The object is to solve for x. (Sometimes it's y or z, or some other variable.)
------------
There's more than 1 way to do that, but the quadratic equation always works.
--------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A2%2A-3=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+0.5
x%5B2%5D+=+%28-%285%29-sqrt%28+49+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B5x%2B-3 can be factored:
2x%5E2%2B5x%2B-3+=+%28x-0.5%29%2A%28x--3%29
Again, the answer is: 0.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-3+%29

===================
Reply via the TY note if you have more questions.